Note on Stretching of Line and Surface Elements in Isotropic Turbulence

Abstract

Certain inequalities are rigorously established connecting the statistical stretching of line and surface elements with the statistical dilatation of volume in a compressible fluid in isotropic turbulent motion. The method of approach differs only slightly from those used by Cocke (1969) and by Orszag (1970) for the incompressible case, the only novel feature being the introduction of the general theory of isotropic tensors. In the incompressible case, the earlier results are reproduced in the form given by Orszag.